%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:26:12 PM UTC 2026
% Result : Theorem 0.09s 0.61s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n001.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sun Sep 20 14:13:57 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 0.09/0.61 % Refutation found
% 0.09/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.61 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.61 fof(f1,axiom,(
% 0.09/0.61 (! [X,Y] :( unequally_directed_opposite_lines(X,Y)<=> unequally_directed_lines(X,reverse_line(Y)) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f4,axiom,(
% 0.09/0.61 (! [X,Y] :( equally_directed_lines(X,Y)<=> ~ unequally_directed_lines(X,Y) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f5,axiom,(
% 0.09/0.61 (! [X,Y] :( equally_directed_opposite_lines(X,Y)<=> ~ unequally_directed_opposite_lines(X,Y) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f16,axiom,(
% 0.09/0.61 (! [L,M,N] :( unequally_directed_lines(L,M)=> ( unequally_directed_lines(L,N)| unequally_directed_lines(M,N) ) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f18,axiom,(
% 0.09/0.61 (! [L,M] :( unequally_directed_lines(L,M)| unequally_directed_lines(L,reverse_line(M)) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f19,axiom,(
% 0.09/0.61 (! [L,M] :( ( unequally_directed_lines(L,M)& unequally_directed_lines(L,reverse_line(M)) )=> ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f21,axiom,(
% 0.09/0.61 (! [L,M] :~ ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f37,conjecture,(
% 0.09/0.61 (! [L,M,N] :( ( equally_directed_opposite_lines(L,M)& equally_directed_lines(L,N) )=> equally_directed_opposite_lines(M,N) ) )),
% 0.09/0.61 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.61 fof(f38,negated_conjecture,(
% 0.09/0.61 ~((! [L,M,N] :( ( equally_directed_opposite_lines(L,M)& equally_directed_lines(L,N) )=> equally_directed_opposite_lines(M,N) ) ))),
% 0.09/0.61 inference(negated_conjecture,[status(cth)],[f37])).
% 0.09/0.61 fof(f39,plain,(
% 0.09/0.61 ![X,Y]: ((~unequally_directed_opposite_lines(X,Y)|unequally_directed_lines(X,reverse_line(Y)))&(unequally_directed_opposite_lines(X,Y)|~unequally_directed_lines(X,reverse_line(Y))))),
% 0.09/0.61 inference(NNF_transformation,[status(thm)],[f1])).
% 0.09/0.61 fof(f40,plain,(
% 0.09/0.61 (![X,Y]: (~unequally_directed_opposite_lines(X,Y)|unequally_directed_lines(X,reverse_line(Y))))&(![X,Y]: (unequally_directed_opposite_lines(X,Y)|~unequally_directed_lines(X,reverse_line(Y))))),
% 0.09/0.61 inference(miniscoping,[status(thm)],[f39])).
% 0.09/0.61 fof(f41,plain,(
% 0.09/0.61 ![X0,X1]: (~unequally_directed_opposite_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.61 fof(f42,plain,(
% 0.09/0.61 ![X0,X1]: (unequally_directed_opposite_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f40])).
% 0.09/0.61 fof(f51,plain,(
% 0.09/0.61 ![X,Y]: ((~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y))&(equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.09/0.61 inference(NNF_transformation,[status(thm)],[f4])).
% 0.09/0.61 fof(f52,plain,(
% 0.09/0.61 (![X,Y]: (~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y)))&(![X,Y]: (equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.09/0.61 inference(miniscoping,[status(thm)],[f51])).
% 0.09/0.61 fof(f53,plain,(
% 0.09/0.61 ![X0,X1]: (~equally_directed_lines(X0,X1)|~unequally_directed_lines(X0,X1))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f52])).
% 0.09/0.61 fof(f54,plain,(
% 0.09/0.61 ![X0,X1]: (equally_directed_lines(X0,X1)|unequally_directed_lines(X0,X1))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f52])).
% 0.09/0.61 fof(f55,plain,(
% 0.09/0.61 ![X,Y]: ((~equally_directed_opposite_lines(X,Y)|~unequally_directed_opposite_lines(X,Y))&(equally_directed_opposite_lines(X,Y)|unequally_directed_opposite_lines(X,Y)))),
% 0.09/0.61 inference(NNF_transformation,[status(thm)],[f5])).
% 0.09/0.61 fof(f56,plain,(
% 0.09/0.61 (![X,Y]: (~equally_directed_opposite_lines(X,Y)|~unequally_directed_opposite_lines(X,Y)))&(![X,Y]: (equally_directed_opposite_lines(X,Y)|unequally_directed_opposite_lines(X,Y)))),
% 0.09/0.61 inference(miniscoping,[status(thm)],[f55])).
% 0.09/0.61 fof(f57,plain,(
% 0.09/0.61 ![X0,X1]: (~equally_directed_opposite_lines(X0,X1)|~unequally_directed_opposite_lines(X0,X1))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f56])).
% 0.09/0.61 fof(f58,plain,(
% 0.09/0.61 ![X0,X1]: (equally_directed_opposite_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f56])).
% 0.09/0.61 fof(f101,plain,(
% 0.09/0.61 ![L,M,N]: (~unequally_directed_lines(L,M)|(unequally_directed_lines(L,N)|unequally_directed_lines(M,N)))),
% 0.09/0.61 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.09/0.61 fof(f102,plain,(
% 0.09/0.61 ![L,M]: (~unequally_directed_lines(L,M)|(![N]: (unequally_directed_lines(L,N)|unequally_directed_lines(M,N))))),
% 0.09/0.61 inference(miniscoping,[status(thm)],[f101])).
% 0.09/0.61 fof(f103,plain,(
% 0.09/0.61 ![X0,X1,X2]: (~unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,X2)|unequally_directed_lines(X1,X2))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f102])).
% 0.09/0.61 fof(f110,plain,(
% 0.09/0.61 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f18])).
% 0.09/0.61 fof(f111,plain,(
% 0.09/0.61 ![L,M]: ((~unequally_directed_lines(L,M)|~unequally_directed_lines(L,reverse_line(M)))|(left_convergent_lines(L,M)|left_convergent_lines(L,reverse_line(M))))),
% 0.09/0.61 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.09/0.61 fof(f112,plain,(
% 0.09/0.61 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,X1)|left_convergent_lines(X0,reverse_line(X1)))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f111])).
% 0.09/0.61 fof(f117,plain,(
% 0.09/0.61 ![L,M]: (~left_convergent_lines(L,M)&~left_convergent_lines(L,reverse_line(M)))),
% 0.09/0.61 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.09/0.61 fof(f118,plain,(
% 0.09/0.61 (![L,M]: ~left_convergent_lines(L,M))&(![L,M]: ~left_convergent_lines(L,reverse_line(M)))),
% 0.09/0.61 inference(miniscoping,[status(thm)],[f117])).
% 0.09/0.61 fof(f119,plain,(
% 0.09/0.61 ![X0,X1]: (~left_convergent_lines(X0,X1))),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f118])).
% 0.09/0.61 fof(f152,plain,(
% 0.09/0.61 (?[L,M,N]: ((equally_directed_opposite_lines(L,M)&equally_directed_lines(L,N))&~equally_directed_opposite_lines(M,N)))),
% 0.09/0.61 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.09/0.61 fof(f153,plain,(
% 0.09/0.61 ?[M,N]: ((?[L]: (equally_directed_opposite_lines(L,M)&equally_directed_lines(L,N)))&~equally_directed_opposite_lines(M,N))),
% 0.09/0.61 inference(miniscoping,[status(thm)],[f152])).
% 0.09/0.61 fof(f154,plain,(
% 0.09/0.61 ((equally_directed_opposite_lines(sK2_skl,sK0_skl)&equally_directed_lines(sK2_skl,sK1_skl))&~equally_directed_opposite_lines(sK0_skl,sK1_skl))),
% 0.09/0.61 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(M,sK0_skl),skolemize(N,sK1_skl),skolemize(L,sK2_skl)],[f153])).
% 0.09/0.61 fof(f155,plain,(
% 0.09/0.61 equally_directed_opposite_lines(sK2_skl,sK0_skl)),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f154])).
% 0.09/0.61 fof(f156,plain,(
% 0.09/0.61 equally_directed_lines(sK2_skl,sK1_skl)),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f154])).
% 0.09/0.61 fof(f157,plain,(
% 0.09/0.61 ~equally_directed_opposite_lines(sK0_skl,sK1_skl)),
% 0.09/0.61 inference(cnf_transformation,[status(thm)],[f154])).
% 0.09/0.61 fof(f163,plain,(
% 0.09/0.61 unequally_directed_opposite_lines(sK0_skl,sK1_skl)),
% 0.09/0.61 inference(resolution,[status(thm)],[f58,f157])).
% 0.09/0.61 fof(f165,plain,(
% 0.09/0.61 ![X0,X1]: (~unequally_directed_opposite_lines(X0,X1)|~equally_directed_lines(X0,reverse_line(X1)))),
% 0.09/0.61 inference(resolution,[status(thm)],[f41,f53])).
% 0.09/0.61 fof(f168,plain,(
% 0.09/0.61 ~equally_directed_lines(sK0_skl,reverse_line(sK1_skl))),
% 0.09/0.61 inference(resolution,[status(thm)],[f165,f163])).
% 0.09/0.61 fof(f169,plain,(
% 0.09/0.61 unequally_directed_lines(sK0_skl,reverse_line(sK1_skl))),
% 0.09/0.61 inference(resolution,[status(thm)],[f168,f54])).
% 0.09/0.61 fof(f174,plain,(
% 0.09/0.61 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.09/0.61 inference(resolution,[status(thm)],[f110,f42])).
% 0.09/0.61 fof(f242,plain,(
% 0.09/0.61 ![X0,X1,X2]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(X2,X1)|unequally_directed_opposite_lines(X0,X2))),
% 0.09/0.61 inference(resolution,[status(thm)],[f103,f174])).
% 0.09/0.61 fof(f303,plain,(
% 0.09/0.61 ![X0,X1,X2]: (unequally_directed_lines(X0,X1)|unequally_directed_opposite_lines(X2,X0)|~equally_directed_lines(X2,X1))),
% 0.09/0.61 inference(resolution,[status(thm)],[f242,f53])).
% 0.09/0.61 fof(f314,plain,(
% 0.09/0.61 ![X0]: (unequally_directed_lines(X0,sK1_skl)|unequally_directed_opposite_lines(sK2_skl,X0))),
% 0.09/0.61 inference(resolution,[status(thm)],[f303,f156])).
% 0.09/0.62 fof(f467,definition,(
% 0.09/0.62 sQ12_spl <=> (unequally_directed_lines(sK0_skl,sK1_skl))),
% 0.09/0.62 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.09/0.62 fof(f468,plain,(
% 0.09/0.62 unequally_directed_lines(sK0_skl,sK1_skl)|~sQ12_spl),
% 0.09/0.62 inference(component_clause,[status(thm)],[f467])).
% 0.09/0.62 fof(f469,plain,(
% 0.09/0.62 ~unequally_directed_lines(sK0_skl,sK1_skl)|sQ12_spl),
% 0.09/0.62 inference(component_clause,[status(thm)],[f467])).
% 0.09/0.62 fof(f528,plain,(
% 0.09/0.62 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,reverse_line(X1)))),
% 0.09/0.62 inference(forward_subsumption_resolution,[status(thm)],[f112,f119])).
% 0.09/0.62 fof(f529,plain,(
% 0.09/0.62 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.09/0.62 inference(resolution,[status(thm)],[f528,f119])).
% 0.09/0.62 fof(f532,plain,(
% 0.09/0.62 unequally_directed_opposite_lines(sK2_skl,sK0_skl)|sQ12_spl),
% 0.09/0.62 inference(resolution,[status(thm)],[f469,f314])).
% 0.09/0.62 fof(f647,plain,(
% 0.09/0.62 ~equally_directed_opposite_lines(sK2_skl,sK0_skl)|sQ12_spl),
% 0.09/0.62 inference(resolution,[status(thm)],[f532,f57])).
% 0.09/0.62 fof(f648,plain,(
% 0.09/0.62 $false|sQ12_spl),
% 0.09/0.62 inference(forward_subsumption_resolution,[status(thm)],[f647,f155])).
% 0.09/0.62 fof(f649,plain,(
% 0.09/0.62 sQ12_spl),
% 0.09/0.62 inference(contradiction_clause,[status(thm)],[f648])).
% 0.09/0.62 fof(f739,plain,(
% 0.09/0.62 ~unequally_directed_lines(sK0_skl,sK1_skl)),
% 0.09/0.62 inference(resolution,[status(thm)],[f529,f169])).
% 0.09/0.62 fof(f766,plain,(
% 0.09/0.62 $false|~sQ12_spl),
% 0.09/0.62 inference(forward_subsumption_resolution,[status(thm)],[f739,f468])).
% 0.09/0.62 fof(f767,plain,(
% 0.09/0.62 ~sQ12_spl),
% 0.09/0.62 inference(contradiction_clause,[status(thm)],[f766])).
% 0.09/0.62 fof(f768,plain,(
% 0.09/0.62 $false),
% 0.09/0.62 inference(sat_refutation,[status(thm)],[f649,f767])).
% 0.09/0.62 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.64 % Elapsed time: 0.056658 seconds
% 0.14/0.64 % CPU time: 0.205995 seconds
% 0.14/0.64 % Total memory used: 14.892 MB
% 0.14/0.64 % Net memory used: 14.574 MB
%------------------------------------------------------------------------------